Conformal Kaehler Euclidean submanifolds

A. de Carvalho; S. Chion; M. Dajczer

doi:10.1016/j.difgeo.2022.101893

Conformal Kaehler Euclidean submanifolds

A. de Carvalho
, S. Chion
, M. Dajczer

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

3 Citas (Scopus)

Resumen

Let f:M²ⁿ→R^2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M²ⁿ is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M²ⁿ into either R²ⁿ⁺¹ or R²ⁿ⁺², the latter being a class of submanifolds already extensively studied.

Idioma original	Inglés
Número de artículo	101893
Publicación	Differential Geometry and its Application
Volumen	82
DOI	https://doi.org/10.1016/j.difgeo.2022.101893
Estado	Publicada - jun. 2022
Publicado de forma externa	Sí

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@article{54582d333afa44f3b480beb35ff9d65b,

title = "Conformal Kaehler Euclidean submanifolds",

abstract = "Let f:M2n→R2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M2n is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M2n into either R2n+1 or R2n+2, the latter being a class of submanifolds already extensively studied.",

keywords = "Conformal congruence, Conformal immersion, Real Kaehler submanifold",

author = "\{de Carvalho\}, A. and S. Chion and M. Dajczer",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

month = jun,

doi = "10.1016/j.difgeo.2022.101893",

language = "English",

volume = "82",

journal = "Differential Geometry and its Application",

issn = "0926-2245",

}

TY - JOUR

T1 - Conformal Kaehler Euclidean submanifolds

AU - de Carvalho, A.

AU - Chion, S.

AU - Dajczer, M.

PY - 2022/6

Y1 - 2022/6

N2 - Let f:M2n→R2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M2n is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M2n into either R2n+1 or R2n+2, the latter being a class of submanifolds already extensively studied.

AB - Let f:M2n→R2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M2n is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M2n into either R2n+1 or R2n+2, the latter being a class of submanifolds already extensively studied.

KW - Conformal congruence

KW - Conformal immersion

KW - Real Kaehler submanifold

UR - https://www.scopus.com/pages/publications/85129467950

U2 - 10.1016/j.difgeo.2022.101893

DO - 10.1016/j.difgeo.2022.101893

M3 - Article

AN - SCOPUS:85129467950

SN - 0926-2245

VL - 82

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

M1 - 101893

ER -

Conformal Kaehler Euclidean submanifolds

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